Post-inflationary axions: a minimal target for axion haloscopes

An axion-like-particle (ALP) in the post-inflationary scenario with domain wall number $N>1$ can be dark matter if the residual $\mathbb{Z}_N$ symmetry has a small explicit breaking. Although we cannot determine the full dynamics of the system reliably, we provide evidence that such an ALP can account for the observed dark matter abundance while having a relatively small decay constant and consequently a possibly large coupling to photons. In particular, we determine the number of domain walls per Hubble patch around the time when they form using numerical simulations and combine this with analytic expectations about the subsequent dynamics. We show that the strongest constraint on the decay constant is likely to come from the dark matter ALPs being produced with large isocurvature fluctuations at small spatial scales. We also comment on the uncertainties on the dark matter small-scale structure that might form from these overdensities, in particular pointing out the importance of quantum pressure in the $N=1$ case.